7,033 research outputs found
Variable Regularized Fast Affine Projections
This paper introduces a variable regularization method for the fast affine projection algorithm (VR-FAP). It is inspired by a recently introduced technique for variable regularization of the classical, affine projection algorithm (VR-APA). In both algorithms, the regularization parameter varies as a function of the excitation, measurement noise, and residual error energies. Because of the dependence on the last parameter, VR-APA and VR-FAP demonstrate the desirable property of fast convergence (via a small regularization value) when the convergence is poor and deep convergence/immunity to measurement noise (via a large regularization value) when the convergence is good. While the regularization parameter of APA is explicitly available for on-line modification, FAP\u27s regularization is only set at initialization. To overcome this problem we use noise-injection with the noise-power proportional to the variable regularization parameter. As with their fixed regularization versions, VR-FAP is considerably less complex than VR-APA and simulations verify that they have the very similar convergence propertie
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
An Improved Observation Model for Super-Resolution under Affine Motion
Super-resolution (SR) techniques make use of subpixel shifts between frames
in an image sequence to yield higher-resolution images. We propose an original
observation model devoted to the case of non isometric inter-frame motion as
required, for instance, in the context of airborne imaging sensors. First, we
describe how the main observation models used in the SR literature deal with
motion, and we explain why they are not suited for non isometric motion. Then,
we propose an extension of the observation model by Elad and Feuer adapted to
affine motion. This model is based on a decomposition of affine transforms into
successive shear transforms, each one efficiently implemented by row-by-row or
column-by-column 1-D affine transforms.
We demonstrate on synthetic and real sequences that our observation model
incorporated in a SR reconstruction technique leads to better results in the
case of variable scale motions and it provides equivalent results in the case
of isometric motions
Solving ill-posed inverse problems using iterative deep neural networks
We propose a partially learned approach for the solution of ill posed inverse
problems with not necessarily linear forward operators. The method builds on
ideas from classical regularization theory and recent advances in deep learning
to perform learning while making use of prior information about the inverse
problem encoded in the forward operator, noise model and a regularizing
functional. The method results in a gradient-like iterative scheme, where the
"gradient" component is learned using a convolutional network that includes the
gradients of the data discrepancy and regularizer as input in each iteration.
We present results of such a partially learned gradient scheme on a non-linear
tomographic inversion problem with simulated data from both the Sheep-Logan
phantom as well as a head CT. The outcome is compared against FBP and TV
reconstruction and the proposed method provides a 5.4 dB PSNR improvement over
the TV reconstruction while being significantly faster, giving reconstructions
of 512 x 512 volumes in about 0.4 seconds using a single GPU
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